Solve for $x$ : $x^2 - 4x - 5 = 0$
Solution: The coefficient on the $x$ term is $-4$ and the constant term is $-5$ , so we need to find two numbers that add up to $-4$ and multiply to $-5$ The two numbers $-5$ and $1$ satisfy both conditions: $ {-5} + {1} = {-4} $ $ {-5} \times {1} = {-5} $ $(x {-5}) (x + {1}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -5) (x + 1) = 0$ $x - 5 = 0$ or $x + 1 = 0$ Thus, $x = 5$ and $x = -1$ are the solutions.